1. Field of the Invention
The present invention relates generally to computer interfaces, such as keypads, keyboards and the like, and particularly to a computer interface having a circular arrangement of keys.
2. Description of the Related Art
In music theory, the circle of fifths (or circle of fourths) is a visual representation of the relationships among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys. More specifically, it is a geometrical representation of relationships among the 12 pitch classes of the chromatic scale in pitch class space. FIG. 2 illustrates the conventional circle of fifths arrangement, showing major and minor keys. The term “fifth” defines an interval or mathematical ratio which is the closest and most consonant non-octave interval. The circle of fifths is a sequence of pitches or key tonalities, represented as a circle, in which the next pitch is found seven semitones higher than the last. Musicians and composers use the circle of fifths to understand and describe the musical relationships among some selection of those pitches. The circle's design is helpful in composing and harmonizing melodies, building chords, and modulating to different keys within a composition.
At the top of the circle, the key of C Major has no sharps or flats. Starting from the apex and proceeding clockwise by ascending fifths, the key of G has one sharp, the key of D has 2 sharps, and so on. Similarly, proceeding counterclockwise from the apex by descending fifths, the key of F has one flat, the key of B ♭ has 2 flats, and so on. At the bottom of the circle, the sharp and flat keys overlap, showing pairs of enharmonic key signatures.
Starting at any pitch, ascending by the interval of an equal tempered fifth, one passes all twelve tones clockwise, to return to the beginning pitch class. To pass the twelve tones counterclockwise, it is necessary to ascend by perfect fourths, rather than fifths. FIG. 3 shows the circle of fifths drawn within the chromatic circle as a star dodecagram. The circle of fifths is closely related to the chromatic circle, which also arranges the twelve equal-tempered pitch classes in a circular ordering. A key difference between the two circles is that the chromatic circle can be understood as a continuous space where every point on the circle corresponds to a conceivable pitch class, and every conceivable pitch class corresponds to a point on the circle. By contrast, the circle of fifths is fundamentally a discrete structure, and there is no obvious way to assign pitch classes to each of its points. In this sense, the two circles are mathematically quite different.
However, the twelve equal-tempered pitch classes can be represented by the cyclic group of order twelve, or equivalently, the residue classes modulo twelve, Z/12Z. The group Z12 has four generators, which can be identified with the ascending and descending semitones and the ascending and descending perfect fifths. The semitonal generator gives rise to the chromatic circle while the perfect fifth gives rise to the circle of fifths. The circle of fifths, or fourths, can be mapped from the chromatic scale by multiplication, and vice versa. To map between the circle of fifths and the chromatic scale (in integer notation) multiply by 7 (M7), and for the circle of fourths multiply by 5 (P5).
A simple way to see the musical interval known as a fifth is by looking at a piano keyboard, and, starting at any key, counting seven keys to the right (both black and white) to get to the next note on the circle shown in FIG. 2. Seven half steps, the distance from the first to the eighth key on a piano is a “perfect fifth”, called “perfect” because it is neither major nor minor, but applies to both major and minor scales and chords, and a “fifth” because though it is a distance of seven semitones on a keyboard, it is a distance of five steps within a major or minor scale. A simple way to hear the relationship between these notes is by playing them on a piano keyboard. If you traverse the circle of fifths backwards, the notes will feel as though they fall into each other. This aural relationship is what the mathematics describes. Despite the simplicity and usefulness of the circle of fifths (and its related chromatic scale), one must perform mental and mathematical operations, as described above, in order to translate the circle of fifths onto an actual musical instrument. It would therefore be desirable to be able to provide an arrangement of keys which directly translates to the circle of fifths, and vice versa.
Thus, a circular computer interface addressing the aforementioned problems is desired.